The 56-year-old was reported missing after she was last seen at 8am on Tuesday, according to a family member.
In an update released by West Yorkshire Police on Wednesday evening, a spokesman said a body had been found in the search, although did not disclose where the discovery had been made.
Her family have been informed of the discovery and the death is not believed to be suspicious.
The spokesman said: "Although formal identification hasn’t taken place the family of Beverley O’Connor have been made aware of the development and police are continuing to offer support to the family.
"There are not thought to be any suspicious circumstances surrounding the death and a file will be prepared for the coroner."